Acta Geophysica

, Volume 61, Issue 6, pp 1351–1394 | Cite as

Fitting and goodness-of-fit test of non-truncated and truncated power-law distributions

  • Anna Deluca
  • Álvaro Corral
Research Article


Recently, Clauset, Shalizi, and Newman have proposed a systematic method to find over which range (if any) a certain distribution behaves as a power law. However, their method has been found to fail, in the sense that true (simulated) power-law tails are not recognized as such in some instances, and then the power-law hypothesis is rejected. Moreover, the method does not work well when extended to power-law distributions with an upper truncation. We explain in detail a similar but alternative procedure, valid for truncated as well as for non-truncated power-law distributions, based in maximum likelihood estimation, the Kolmogorov-Smirnov goodness-of-fit test, and Monte Carlo simulations. An overview of the main concepts as well as a recipe for their practical implementation is provided. The performance of our method is put to test on several empirical data which were previously analyzed with less systematic approaches. We find the functioning of the method very satisfactory.

Key words

power-law distribution estimation goodness-of-fit tests binning seismic-moment distribution waiting-time distribution tropicalcyclone energy 


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© Versita Warsaw and Springer-Verlag Wien 2013

Authors and Affiliations

  1. 1.Centre de Recerca MatemàticaBellaterra, BarcelonaSpain
  2. 2.Departament de MatemàtiquesUniversitat Autònoma de BarcelonaCerdanyolaSpain

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